Yue Kang

Yue Kang, Cho-Jui Hsieh, Thomas C. M. Lee

In stochastic contextual bandits, an agent sequentially makes actions from a time-dependent action set based on past experience to minimize the cumulative regret. Like many other machine learning algorithms, the performance of bandits heavily depends on the values of hyperparameters, and theoretically derived parameter values may lead to unsatisfactory results in practice. Moreover, it is infeasible to use offline tuning methods like cross-validation to choose hyperparameters under the bandit environment, as the decisions should be made in real-time. To address this challenge, we propose the first online continuous hyperparameter tuning framework for contextual bandits to learn the optimal parameter configuration in practice within a search space on the fly. Specifically, we use a double-layer bandit framework named CDT (Continuous Dynamic Tuning) and formulate the hyperparameter optimization as a non-stationary continuum-armed bandit, where each arm represents a combination of hyperparameters, and the corresponding reward is the algorithmic result. For the top layer, we propose the Zooming TS algorithm that utilizes Thompson Sampling (TS) for exploration and a restart technique to get around the \textit{switching} environment. The proposed CDT framework can be easily utilized to tune contextual bandit algorithms without any pre-specified candidate set for multiple hyperparameters. We further show that it could achieve a sublinear regret in theory and performs consistently better than all existing methods on both synthetic and real datasets.

Bongsoo Yi, Yue Kang, Yao Li

The dueling bandit problem, an essential variation of the traditional multi-armed bandit problem, has become significantly prominent recently due to its broad applications in online advertising, recommendation systems, information retrieval, and more. However, in many real-world applications, the feedback for actions is often subject to unavoidable delays and is not immediately available to the agent. This partially observable issue poses a significant challenge to existing dueling bandit literature, as it significantly affects how quickly and accurately the agent can update their policy on the fly. In this paper, we introduce and examine the biased dueling bandit problem with stochastic delayed feedback, revealing that this new practical problem will delve into a more realistic and intriguing scenario involving a preference bias between the selections. We present two algorithms designed to handle situations involving delay. Our first algorithm, requiring complete delay distribution information, achieves the optimal regret bound for the dueling bandit problem when there is no delay. The second algorithm is tailored for situations where the distribution is unknown, but only the expected value of delay is available. We provide a comprehensive regret analysis for the two proposed algorithms and then evaluate their empirical performance on both synthetic and real datasets.

Yue Kang, Cho-Jui Hsieh, Thomas C. M. Lee

In the stochastic contextual low-rank matrix bandit problem, the expected reward of an action is given by the inner product between the action's feature matrix and some fixed, but initially unknown $d_1$ by $d_2$ matrix $Θ^*$ with rank $r \ll \{d_1, d_2\}$, and an agent sequentially takes actions based on past experience to maximize the cumulative reward. In this paper, we study the generalized low-rank matrix bandit problem, which has been recently proposed in \cite{lu2021low} under the Generalized Linear Model (GLM) framework. To overcome the computational infeasibility and theoretical restrain of existing algorithms on this problem, we first propose the G-ESTT framework that modifies the idea from \cite{jun2019bilinear} by using Stein's method on the subspace estimation and then leverage the estimated subspaces via a regularization idea. Furthermore, we remarkably improve the efficiency of G-ESTT by using a novel exclusion idea on the estimated subspace instead, and propose the G-ESTS framework. We also show that G-ESTT can achieve the $\tilde{O}(\sqrt{(d_1+d_2)MrT})$ bound of regret while G-ESTS can achineve the $\tilde{O}(\sqrt{(d_1+d_2)^{3/2}Mr^{3/2}T})$ bound of regret under mild assumption up to logarithm terms, where $M$ is some problem dependent value. Under a reasonable assumption that $M = O((d_1+d_2)^2)$ in our problem setting, the regret of G-ESTT is consistent with the current best regret of $\tilde{O}((d_1+d_2)^{3/2} \sqrt{rT}/D_{rr})$~\citep{lu2021low} ($D_{rr}$ will be defined later). For completeness, we conduct experiments to illustrate that our proposed algorithms, especially G-ESTS, are also computationally tractable and consistently outperform other state-of-the-art (generalized) linear matrix bandit methods based on a suite of simulations.

Yue Kang, Cho-Jui Hsieh, Thomas C. M. Lee

In stochastic low-rank matrix bandit, the expected reward of an arm is equal to the inner product between its feature matrix and some unknown $d_1$ by $d_2$ low-rank parameter matrix $Θ^*$ with rank $r \ll d_1\wedge d_2$. While all prior studies assume the payoffs are mixed with sub-Gaussian noises, in this work we loosen this strict assumption and consider the new problem of \underline{low}-rank matrix bandit with \underline{h}eavy-\underline{t}ailed \underline{r}ewards (LowHTR), where the rewards only have finite $(1+δ)$ moment for some $δ\in (0,1]$. By utilizing the truncation on observed payoffs and the dynamic exploration, we propose a novel algorithm called LOTUS attaining the regret bound of order $\tilde O(d^\frac{3}{2}r^\frac{1}{2}T^\frac{1}{1+δ}/\tilde{D}_{rr})$ without knowing $T$, which matches the state-of-the-art regret bound under sub-Gaussian noises~\citep{lu2021low,kang2022efficient} with $δ= 1$. Moreover, we establish a lower bound of the order $Ω(d^\fracδ{1+δ} r^\fracδ{1+δ} T^\frac{1}{1+δ}) = Ω(T^\frac{1}{1+δ})$ for LowHTR, which indicates our LOTUS is nearly optimal in the order of $T$. In addition, we improve LOTUS so that it does not require knowledge of the rank $r$ with $\tilde O(dr^\frac{3}{2}T^\frac{1+δ}{1+2δ})$ regret bound, and it is efficient under the high-dimensional scenario. We also conduct simulations to demonstrate the practical superiority of our algorithm.

Bongsoo Yi, Yue Kang, Yao Li

The Lipschitz bandit is a key variant of stochastic bandit problems where the expected reward function satisfies a Lipschitz condition with respect to an arm metric space. With its wide-ranging practical applications, various Lipschitz bandit algorithms have been developed, achieving the cumulative regret lower bound of order $\tilde O(T^{(d_z+1)/(d_z+2)})$ over time horizon $T$. Motivated by recent advancements in quantum computing and the demonstrated success of quantum Monte Carlo in simpler bandit settings, we introduce the first quantum Lipschitz bandit algorithms to address the challenges of continuous action spaces and non-linear reward functions. Specifically, we first leverage the elimination-based framework to propose an efficient quantum Lipschitz bandit algorithm named Q-LAE. Next, we present novel modifications to the classical Zooming algorithm, which results in a simple quantum Lipschitz bandit method, Q-Zooming. Both algorithms exploit the computational power of quantum methods to achieve an improved regret bound of $\tilde O(T^{d_z/(d_z+1)})$. Comprehensive experiments further validate our improved theoretical findings, demonstrating superior empirical performance compared to existing Lipschitz bandit methods.

Zhuoyi Huang, Nutan Sahoo, Anamika Kumari et al. · stanford

The development of machine learning for cardiac care is severely hampered by privacy restrictions on sharing real patient electrocardiogram (ECG) data. Although generative AI offers a promising solution, the real-world use of existing model-synthesized ECGs is limited by persistent gaps in trustworthiness and clinical utility. In this work, we address two major shortcomings of current generative ECG methods: insufficient morphological fidelity and the inability to generate personalized, patient-specific physiological signals. To address these gaps, we build on a conditional diffusion-based Structured State Space Model (SSSD-ECG) with two principled innovations: (1) MIDT-ECG (Mel-Spectrogram Informed Diffusion Training), a novel training paradigm with time-frequency domain supervision to enforce physiological structural realism, and (2) multi-modal demographic conditioning to enable patient-specific synthesis. We comprehensively evaluate our approach on the PTB-XL dataset, assessing the synthesized ECG signals on fidelity, clinical coherence, privacy preservation, and downstream task utility. MIDT-ECG achieves substantial gains: it improves morphological coherence, preserves strong privacy guarantees with all metrics evaluated exceeding the baseline by 4-8%, and notably reduces the interlead correlation error by an average of 74%, while demographic conditioning enhances signal-to-noise ratio and personalization. In critical low-data regimes, a classifier trained on datasets supplemented with our synthetic ECGs achieves performance comparable to a classifier trained solely on real data. Together, we demonstrate that ECG synthesizers, trained with the proposed time-frequency structural regularization scheme, can serve as personalized, high-fidelity, privacy-preserving surrogates when real data are scarce, advancing the responsible use of generative AI in healthcare.

Zhongxuan Liu, Yue Kang, Thomas C. M. Lee

The Lipschitz bandit problem extends stochastic bandits to a continuous action set defined over a metric space, where the expected reward function satisfies a Lipschitz condition. In this work, we introduce a new problem of Lipschitz bandit in the presence of stochastic delayed feedback, where the rewards are not observed immediately but after a random delay. We consider both bounded and unbounded stochastic delays, and design algorithms that attain sublinear regret guarantees in each setting. For bounded delays, we propose a delay-aware zooming algorithm that retains the optimal performance of the delay-free setting up to an additional term that scales with the maximal delay $τ_{\max}$. For unbounded delays, we propose a novel phased learning strategy that accumulates reliable feedback over carefully scheduled intervals, and establish a regret lower bound showing that our method is nearly optimal up to logarithmic factors. Finally, we present experimental results to demonstrate the efficiency of our algorithms under various delay scenarios.

Yue Kang, Cho-Jui Hsieh, Thomas C. M. Lee

Lipschitz bandit is a variant of stochastic bandits that deals with a continuous arm set defined on a metric space, where the reward function is subject to a Lipschitz constraint. In this paper, we introduce a new problem of Lipschitz bandits in the presence of adversarial corruptions where an adaptive adversary corrupts the stochastic rewards up to a total budget $C$. The budget is measured by the sum of corruption levels across the time horizon $T$. We consider both weak and strong adversaries, where the weak adversary is unaware of the current action before the attack, while the strong one can observe it. Our work presents the first line of robust Lipschitz bandit algorithms that can achieve sub-linear regret under both types of adversary, even when the total budget of corruption $C$ is unrevealed to the agent. We provide a lower bound under each type of adversary, and show that our algorithm is optimal under the strong case. Finally, we conduct experiments to illustrate the effectiveness of our algorithms against two classic kinds of attacks.

Yizhou Wang, Yue Kang, Can Qin et al.

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid training of modern deep neural networks. Nevertheless, they are observed to suffer from compromised generalization ability compared with stochastic gradient descent (\textsc{SGD}) and tend to be trapped in local minima at an early stage during training. Intriguingly, we discover that substituting the gradient in the second raw moment estimate term with its momentumized version in \textsc{Adam} can resolve the issue. The intuition is that gradient with momentum contains more accurate directional information and therefore its second moment estimation is a more favorable option for learning rate scaling than that of the raw gradient. Thereby we propose \textsc{AdaMomentum} as a new optimizer reaching the goal of training fast while generalizing much better. We further develop a theory to back up the improvement in generalization and provide convergence guarantees under both convex and nonconvex settings. Extensive experiments on a wide range of tasks and models demonstrate that \textsc{AdaMomentum} exhibits state-of-the-art performance and superior training stability consistently.